Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
368 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 85 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#16812040 | C2 | semidirect |
| 3. C2×#16812031 | C2 | semidirect |
| 4. C2×#16812029 | C2 | semidirect |
| 5. C2×(C2×D107)⋊C8 | C2 | semidirect |
| 6. #20292484 | C2 | semidirect |
| 7. #340×C107 | C2 | semidirect |
| 46. C2×C107⋊C8 | D4 | semidirect |
| 144. C107 | #2034 | semidirect |
| 151. #340 | D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812084 | 2 |
| C2×#16812040 | 2 |
| C2×#16812031 | 2 |
| C2×#16812029 | 2 |
| C2×(C2×D107)⋊C8 | 2 |
| #20292484 | 2 |
| #340×C107 | 2 |
| #2034 | 107 |